New Perspectives in Commutative and Non-commutative Groups

The present talk is meant to be an overview of recent developments in commutative and non-commutative group theory, with a special consideration for the interconnection between abelian and non-abelian groups, group automorphisms and combinatorial properties of finite and infinite groups. In particular, we will present a classification for the so-called metahamiltonian groups (i.e. groups in which every non-abelian subgroup is normal), some new results about groups with finitely many automorphisms and new perspectives on the study of well-known combinatorial constants such as the Davenport constant and the Harborth constant.